What is weightlessness and how is it obtained?
Weightlessness is a condition in which a body feels no force effects. But that does not mean that there are no forces working. The opposite is the case: A body only then is really weightless when it falls freely under the influence of gravity (a place in space that is completely free of gravitational forces only exists theoretically). Maybe this is difficult to understand, but I try to explain it as simple as possible:
Lets say you are in an elevator standing on a scale. It shows your weight. Now the cable of the elevator tears, and you fall into the void together with the elevator. We will neglect the air friction here. What happens?
Gravity accelerates you and the elevator and the scale with the same rate; in the direction of the ground. But there is no force that acts against the acceleration. Because the scale is falling with you and is accelerated in the same rate, it can't show your weight any more. You are weightless.
That's why not only the astronauts in space in their space ship are weightless, but as well the parachutist in free fall, or you while jumping from the 3-meter board in the pool or from the next best stairs...
Here is a very simple experiment that you can do almost everywhere: Put a heavy book on your hand and jump with it from a chair or other elevated point, and in the moment, when you jump (fall), you won't feel the weight of the book.
Possibilities to create zero gravity here on earth
But why are now the astronauts in their spaceship weightless?
Just simple, out of the same reason I explained at the top of the page:
In space you are continuously in free fall. But each time you have fallen a little closer to the Earth you have gone such a distance (the Space Shuttle goes 27000 km/hour) that the curvature of the Earth has been going away from you just as far as you have fallen, you stay at the same altitude, you keep circling around it. The spaceship is falling around Earth forever unless it is slowed down by a counteracting force (e. g. the firing of the retro rockets) which curves the flight path of the spaceship into the direction of the surface of the Earth and in this way ensures that it reaches the Earth's surface sometime.
I have clarified this in the following sketch that shows different flight paths for different release velocities.
The higher the release speed, the farther the flight path goes, until at the right speed it goes around the planet.